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Volumn 44, Issue 3-4, 2006, Pages 397-404

On the mathematical kinetic theory of active particles with discrete states. The derivation of macroscopic equations

Author keywords

Asymptotic limits; Kinetic theory; Multicellular systems; Nonlinear problems

Indexed keywords

ASYMPTOTIC STABILITY; KINETIC THEORY; MATHEMATICAL MODELS; MICROSCOPIC EXAMINATION; NUMERICAL METHODS; PARTICLE SIZE ANALYSIS;

EID: 33744916996     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2006.01.025     Document Type: Article
Times cited : (9)

References (30)
  • 1
    • 2542432804 scopus 로고    scopus 로고
    • Mathematical topics on the modelling of multicellular systems in the competition between tumor and immune cells
    • Bellomo N., Bellouquid A., and Delitala M. Mathematical topics on the modelling of multicellular systems in the competition between tumor and immune cells. Math. Models Methods Appl. Sci. 14 (2004) 1683-1733
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 1683-1733
    • Bellomo, N.1    Bellouquid, A.2    Delitala, M.3
  • 2
    • 27644478289 scopus 로고    scopus 로고
    • Mathematical methods and tools of kinetic theory towards modelling complex biological systems
    • Bellouquid A., and Delitala M. Mathematical methods and tools of kinetic theory towards modelling complex biological systems. Math. Models Methods Appl. Sci. 15 (2005) 1639-1666
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1639-1666
    • Bellouquid, A.1    Delitala, M.2
  • 4
    • 0034917420 scopus 로고    scopus 로고
    • The diffusion limit of transport equations derived from velocity jump processes
    • Hillen T., and Othmer H. The diffusion limit of transport equations derived from velocity jump processes. SIAM J. Appl. Math. 61 (2000) 751-775
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 751-775
    • Hillen, T.1    Othmer, H.2
  • 5
    • 0036553052 scopus 로고    scopus 로고
    • The diffusion limit of transport equations II: chemotaxis equations
    • Othmer H.G., and Hillen T. The diffusion limit of transport equations II: chemotaxis equations. SIAM J. Appl. Math. 62 (2002) 1222-1250
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1222-1250
    • Othmer, H.G.1    Hillen, T.2
  • 6
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems
    • Stevens A. The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems. SIAM J. Appl. Math. 61 (2000) 183-212
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 183-212
    • Stevens, A.1
  • 7
    • 21844472976 scopus 로고    scopus 로고
    • From signal transduction to spatial pattern formation in E. Coli: a paradigm for multi-scale modeling in biology
    • Erban R., and Othmer H.G. From signal transduction to spatial pattern formation in E. Coli: a paradigm for multi-scale modeling in biology. SIAM J. Multiscale Modeling 3 (2005) 362-394
    • (2005) SIAM J. Multiscale Modeling , vol.3 , pp. 362-394
    • Erban, R.1    Othmer, H.G.2
  • 8
    • 1042302643 scopus 로고    scopus 로고
    • From a class of kinetic models to macroscopic equations for multicellular systems in biology
    • Bellomo N., and Bellouquid A. From a class of kinetic models to macroscopic equations for multicellular systems in biology. Discrete Contin. Dyn. Systs Ser. B 4 (2004) 59-80
    • (2004) Discrete Contin. Dyn. Systs Ser. B , vol.4 , pp. 59-80
    • Bellomo, N.1    Bellouquid, A.2
  • 9
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • Lachowicz M. Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours. Math. Models Methods Appl. Sci. 15 (2005) 1667-1683
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1667-1683
    • Lachowicz, M.1
  • 10
    • 30344453406 scopus 로고    scopus 로고
    • On the onset of nonlinearity for diffusion models of binary mixtures of biological materials by asymptotic analysis
    • Bellomo N., and Bellouquid A. On the onset of nonlinearity for diffusion models of binary mixtures of biological materials by asymptotic analysis. Int. J. Nonlinear Mech. 41 (2006) 281-293
    • (2006) Int. J. Nonlinear Mech. , vol.41 , pp. 281-293
    • Bellomo, N.1    Bellouquid, A.2
  • 11
    • 2542448854 scopus 로고    scopus 로고
    • An explicit subparametric spectral element method of lines applied to tumour angiogenesis system of partial differential equations
    • Valenciano J., and Chaplain M.A.J. An explicit subparametric spectral element method of lines applied to tumour angiogenesis system of partial differential equations. Math. Models Methods Appl. Sci. 14 (2004) 165-187
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 165-187
    • Valenciano, J.1    Chaplain, M.A.J.2
  • 12
    • 12144264054 scopus 로고    scopus 로고
    • Analysis of a mathematical model of tumor lymphangiogenesis
    • Friedman A., and Lolas G. Analysis of a mathematical model of tumor lymphangiogenesis. Math. Models Methods Appl. Sci. 15 (2005) 95-108
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 95-108
    • Friedman, A.1    Lolas, G.2
  • 13
    • 27644540984 scopus 로고    scopus 로고
    • A mathematical model for tumor cords incorporating the flow of interstitial fluids
    • Bertuzzi A., Fasano A., and Gandolfi A. A mathematical model for tumor cords incorporating the flow of interstitial fluids. Math. Models Methods Appl. Sci. 15 (2005) 1735-1777
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1735-1777
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 14
    • 27644463491 scopus 로고    scopus 로고
    • Spatio-temporal heterogeneity arising in a mathematical model of cancer invasion of tissue
    • Chaplain M.A.J., and Lolas G. Spatio-temporal heterogeneity arising in a mathematical model of cancer invasion of tissue. Math. Models Methods Appl. Sci. 15 (2005) 1685-1734
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1685-1734
    • Chaplain, M.A.J.1    Lolas, G.2
  • 15
    • 0030417280 scopus 로고    scopus 로고
    • Tumor heterogeneity and progression: conceptual foundation for modeling
    • Greller L., Tobin F., and Poste G. Tumor heterogeneity and progression: conceptual foundation for modeling. Invasion Metastasis 16 (1996) 177-208
    • (1996) Invasion Metastasis , vol.16 , pp. 177-208
    • Greller, L.1    Tobin, F.2    Poste, G.3
  • 16
    • 7244232531 scopus 로고    scopus 로고
    • From discrete kinetic theory and stochastic game theory to modelling complex systems in applied sciences
    • Bertotti M.L., and Delitala M. From discrete kinetic theory and stochastic game theory to modelling complex systems in applied sciences. Math. Models Methods Appl. Sci. 14 (2004) 1061-1084
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 1061-1084
    • Bertotti, M.L.1    Delitala, M.2
  • 17
    • 33645034895 scopus 로고    scopus 로고
    • A. Chauviere, I. Brazzoli, On the discrete kinetic theory for active particles, - mathematical tools, Math. Comput. Modelling (2006) (in press)
  • 18
    • 8744228120 scopus 로고    scopus 로고
    • Analysis of a new model for tumor-immune system competition including long time scale effects
    • Derbel L. Analysis of a new model for tumor-immune system competition including long time scale effects. Math. Models Methods Appl. Sci. 14 (2004) 1657-1681
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 1657-1681
    • Derbel, L.1
  • 20
    • 27644491983 scopus 로고    scopus 로고
    • Preface and special issue on "Multiscale Cancer Modelling - A New Frontier in Applied Mathematics"
    • Bellomo N., and Maini P.K. Preface and special issue on "Multiscale Cancer Modelling - A New Frontier in Applied Mathematics". Math. Models Methods Appl. Sci. 15 (2005) iii-viii
    • (2005) Math. Models Methods Appl. Sci. , vol.15
    • Bellomo, N.1    Maini, P.K.2
  • 21
    • 0035942758 scopus 로고    scopus 로고
    • A question of scale
    • Vicsek T. A question of scale. Nature 411 (2001) 421
    • (2001) Nature , vol.411 , pp. 421
    • Vicsek, T.1
  • 22
    • 0023746235 scopus 로고
    • Models of dispersed biological systems
    • Othmer H.G., Dunbar S.R., and Alt W. Models of dispersed biological systems. J. Math. Biol. 26 (1988) 263-298
    • (1988) J. Math. Biol. , vol.26 , pp. 263-298
    • Othmer, H.G.1    Dunbar, S.R.2    Alt, W.3
  • 24
    • 7244224708 scopus 로고    scopus 로고
    • Limit behavior of a dense collection of vortex filaments
    • Bessaih H., and Flandoli F. Limit behavior of a dense collection of vortex filaments. Math. Models Methods Appl. Sci. 14 (2004) 189-215
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 189-215
    • Bessaih, H.1    Flandoli, F.2
  • 25
    • 6044260170 scopus 로고    scopus 로고
    • Modelling living fluids with the subdivision into the components in terms of probability distributions
    • Willander M., Mamontov E., and Chiragwandi Z. Modelling living fluids with the subdivision into the components in terms of probability distributions. Math. Models Methods Appl. Sci. 14 (2004) 1495-1520
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 1495-1520
    • Willander, M.1    Mamontov, E.2    Chiragwandi, Z.3
  • 26
    • 0035470907 scopus 로고    scopus 로고
    • Traffic and related self-driven many-particle systems
    • Helbing D. Traffic and related self-driven many-particle systems. Rev. Modern Phys. 73 (2001) 1067-1141
    • (2001) Rev. Modern Phys. , vol.73 , pp. 1067-1141
    • Helbing, D.1
  • 27
    • 0348142119 scopus 로고    scopus 로고
    • Nonlinear models of vehicular traffic flow - new frameworks of the mathematical kinetic theory
    • Delitala M. Nonlinear models of vehicular traffic flow - new frameworks of the mathematical kinetic theory. CR-Mecanique 331 (2003) 817-822
    • (2003) CR-Mecanique , vol.331 , pp. 817-822
    • Delitala, M.1
  • 28
    • 1442333650 scopus 로고    scopus 로고
    • Sociophysics: a personal testimony
    • Galam S. Sociophysics: a personal testimony. Physica A 336 (2003) 49-55
    • (2003) Physica A , vol.336 , pp. 49-55
    • Galam, S.1
  • 29
    • 33645664533 scopus 로고    scopus 로고
    • On the modelling of complex socio-psychological systems with some reasoning about Kate, Jules and Jim
    • Bellomo N., and Carbonaro B. On the modelling of complex socio-psychological systems with some reasoning about Kate, Jules and Jim. Differential Equations Nonlinear Mech. 1 (2006)
    • (2006) Differential Equations Nonlinear Mech. , vol.1
    • Bellomo, N.1    Carbonaro, B.2
  • 30
    • 3543105638 scopus 로고    scopus 로고
    • Evolution of populations playing mixed multiplayer games
    • Platkowski T. Evolution of populations playing mixed multiplayer games. Math. Comput. Modelling 39 (2004) 981-989
    • (2004) Math. Comput. Modelling , vol.39 , pp. 981-989
    • Platkowski, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.